In gas-solid phase exothermic catalytic reactions such as the synthesis of ammonia from hydrogen and nitrogen under pressure, there exists an optimal temperature for fixed pressure and fixed composition of reactant gases, under which temperature the reaction rate is the highest. This optimal temperature, however, decreases as the synthesis rate increases, and with the proceeding of the reaction, the temperature of the catalyst layer will be raised by the continuous releasing of the reaction heat. Thus, in order to improve the efficiency of the reactor, it is necessary to remove the reaction heat out of the reactor. One method that has been widely used is the multi-stage feed-gas-quench reactor, such as the Kellogg four-stage catalyst beds used in large scale ammonia plants. In such systems, feed-gas-quench is used between the stages to reduce the reaction temperature. But as the temperature of the reactant gases is reduced by feed-gas-quench, the concentration of the product of reaction is reduced at the same time, so the synthesis rate is also affected. Improved forms have appeared, in the better ones, the catalyst is divided into three beds. While feed-gas-quench is used between the first and the second section, indirect heat exchange is used between the second and the third section, see, for example, the Chinese patent application CN1030878 filed by the Casale Co. and published on Feb. 8, 1989. The affect on the concentration of the product of reaction by feed-gas-quench has not been completely overcome in this kind of reactors, and the structure of the equipment is made complicated by the adding of indirect heat exchangers between the layer beds.